Low repetition rate spiral microcavity structure and design method

Abstract

The application discloses a low-repetition-frequency spiral microcavity structure and a design method thereof, and belongs to the field of silicon-based integrated photonic chips.The low-repetition-frequency spiral microcavity structure comprises a first spiral curved waveguide, a second spiral curved waveguide, an internal connecting curved waveguide, an external connecting curved waveguide and a bus waveguide.The radius of curvature of each point of the internal connecting curved waveguide changes with the length and satisfies Euler spiral equation, and the internal connecting curved waveguide is used for connecting the starting point of the first spiral curved waveguide and the second spiral curved waveguide.The external connecting curved waveguide is used for connecting the ending point of the first spiral curved waveguide and the second spiral curved waveguide.The first spiral curved waveguide, the second spiral curved waveguide, the internal connecting curved waveguide and the external connecting curved waveguide form a closed spiral ring type waveguide.The light beam transmitted in the bus waveguide is coupled into the spiral ring type waveguide.The application further discloses a design method of the low-repetition-frequency spiral microcavity structure.The application can reduce the loss caused by high-order mode crosstalk and mode mismatch, and improve the chip area utilization.

Description

Technical Field

[0001] This invention belongs to the field of silicon-based integrated photonic chip technology, and relates to a spiral microcavity structure and design method with low repetition rate, low loss and high chip area utilization, which can be applied to chip-based optical atomic clocks, on-chip narrow linewidth lasers and on-chip optical frequency combs. Background Technology

[0002] With the increasing development of integrated photonics technology, high-quality on-chip microring resonator photonic chips have become a hot research area. Silicon nitride, due to its compatibility with CMOS platforms and the absence of two-photon absorption in the communication band, has become the most widely used material. On-chip microring resonators have a wide range of applications, including temperature sensors, magnetic field sensors, gas sensors, angular velocity sensors, distance measurement sensors, and atomic clocks. However, the detection range of photodetectors typically does not exceed 30 GHz. Therefore, designing low-repetition-rate, low-loss microring resonator photonic chips is crucial for realizing miniaturized and integrated optical atomic clocks and other sensors.

[0003] A traditional microring resonator consists of a bus waveguide and a circular waveguide ring. The repetition frequency of the microring resonator is a crucial design parameter, and its value is inversely proportional to the effective length of the microring. For traditional microring cavities, the lower the repetition frequency, the larger the radius of the circular waveguide ring. For example, a traditional microring cavity at 10 GHz has a radius of approximately 2.3 mm, significantly reducing chip area utilization. Furthermore, the quality factor of a microring resonator is primarily related to its losses. Microring losses mainly include absorption loss, scattering loss, bending loss, and losses caused by mode mismatch. Reducing bending loss and mode mismatch loss, especially losses caused by abrupt changes in the microring curvature radius and crosstalk of higher-order modes, is often achieved through optimized microring structure design.

[0004] Existing novel microring resonators often employ a racetrack-shaped structure composed of straight and curved waveguides to reduce losses. The straight waveguide uses a gradually changing width to achieve multimode to single-mode transition, or it can be a single-mode waveguide. The curved waveguide is composed of two symmetrically joined 45° circular arc waveguides, and this waveguide can use either a gradually changing width or a constant width; the curved waveguide can also be constructed with a gradually changing curvature. These solutions still suffer from low chip area utilization and numerous abrupt changes in curvature radius. Therefore, existing low-repetition-rate microring cavities cannot meet the technical requirements of low repetition rate, low loss, and high chip area utilization. Summary of the Invention

[0005] The purpose of this invention is to provide a low-repetition-rate (PRR) helical microcavity structure and its design method. Utilizing a thermally adiabatic bent waveguide with gradually varying curvature, it reduces crosstalk in higher-order modes and losses caused by mode mismatch. Furthermore, it addresses the problem of low chip area utilization in traditional low-PRR microring resonators, thereby improving the chip area utilization of the low-PRR helical microcavity structure. This invention offers the advantages of low loss and high chip area utilization.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses a low-repetition-rate helical microcavity structure, comprising a first helical bent waveguide, a second helical bent waveguide, an internally connecting bent waveguide, an externally connecting bent waveguide, and a bus waveguide. The first helical bent waveguide is a gradually changing radius of curvature, and the second helical bent waveguide is also a gradually changing radius of curvature. The radius of curvature at each point of the internally connecting bent waveguide satisfies the Euler spiral equation as its length changes, and it serves as the starting point connecting the first and second helical bent waveguides. The externally connecting bent waveguide connects the ending points of the first and second helical bent waveguides. The first, second, internally connecting, and externally connecting bent waveguides constitute a closed helical ring waveguide. The bus waveguide transmits the pump laser beam, and the beam transmitted in the bus waveguide is coupled into the helical ring waveguide.

[0008] Furthermore, the beam emitted by the pump laser is transmitted through a bus waveguide, and a portion of the light transmitted through the bus waveguide is coupled into the helical ring waveguide. Since the effective length of the closed helical ring waveguide, composed of the first helical bent waveguide, the second helical bent waveguide, the internally connected bent waveguide, and the externally connected bent waveguide, is calculated according to the free spectral range formula, the first and second helical bent waveguides are structurally arranged using Archimedes' spiral formula, thereby increasing the effective waveguide length while reducing the area, thus improving the chip area utilization of the low-repetition-rate helical microcavity structure. The portion of the light coupled from the bus waveguide into the helical ring waveguide propagates between the first helical bent waveguide, the second helical bent waveguide, the internally connected bent waveguide, and the externally connected bent waveguide, resonating and generating a resonance peak in the output spectrum. Specifically: during the transmission of resonant light in the first helical curved waveguide, the crosstalk loss of higher-order modes during the transmission of resonant light is effectively reduced due to the gradual change in the radius of curvature of the waveguide; during the transmission of resonant light in the second helical curved waveguide, the crosstalk loss of higher-order modes during the transmission of resonant light is reduced due to the gradual change in the radius of curvature of the waveguide; during the transmission of resonant light in the internally connected curved waveguide, the optical mode mismatch loss is reduced because there is no abrupt change in the radius of curvature inside the waveguide, thereby reducing the optical transmission loss of the helical microcavity.

[0009] The formula for the free spectral range is shown in equation (1-1).

[0010]

[0011] Where Δλ represents the FSR of the optical microcavity, L eff n is the length of the optical microcavity. g (λ) is the group refractive index of the waveguide, λ is the wavelength of light, and n eff The effective refractive index.

[0012] The formula for the Archimedes spiral is shown in equation (1-2).

[0013] x=(a+bθ)cosθ (1-2)

[0014] y = (a + bθ)sinθ

[0015] Where a represents the polar radius when θ is 0, b represents the change in polar radius for every 1° of rotation, θ represents the total angle rotated, and the spacing between the spirals is 2πb.

[0016] Furthermore, the internally connected curved waveguide is designed according to the Euler spiral formula (1-3) and is composed of multiple Euler spiral waveguide segments spliced ​​together. The splicing points of adjacent Euler spiral waveguides satisfy the same coordinates (x, y) and the same radius of curvature, thereby ensuring that the radius of curvature changes continuously and slowly at all points of the internally connected curved waveguide, without any regions of abrupt changes in radius of curvature. Moreover, the radius of curvature at each point exhibits multiple change modes, such as gradually increasing, gradually decreasing, and then gradually increasing again.

[0017] The formula for the Euler spiral is shown in equation (1-3).

[0018]

[0019] To reduce the area of ​​the low-repetition-rate (PRR) helical microcavity structure and improve the chip area utilization rate, the external connecting curved waveguide is further constructed from three types of waveguides: straight, Euler spiral, and circular arc. The external connecting curved waveguide is designed as a figure-9 structure, composed of these three types of waveguides. The curvature radius changes abruptly at the connection between the Euler spiral and the circular arc waveguide, but not at the connection between the straight and Euler curves. The curvature radius variation range at the abrupt connection is approximately 5–8 μm. Furthermore, the core material of the first helical curved waveguide, the second helical curved waveguide, the internal connecting curved waveguide, the external connecting curved waveguide, and the bus waveguide is preferably silicon nitride. Based on the material properties of silicon nitride: it has a transparent window in the range of 400 nm to 3.5 μm, enabling use in the visible light to mid-infrared range, meeting the needs of most applications; it has a high nonlinear coefficient and a lower threshold for exciting nonlinear effects, making silicon nitride suitable for the fabrication of microcavity chips.

[0020] This invention discloses a design method for a low repetition rate (PRR) helical microcavity structure, used for designing such a structure. The design method for a low PRR helical microcavity structure includes the following steps:

[0021] Step 1: Determine the waveguide parameters and waveguide spacing of the helical microcavity. The waveguide widths of the first helical bent waveguide, the second helical bent waveguide, the internally connected bent waveguide, and the externally connected bent waveguide are analyzed based on the waveguide characteristics using the finite element method, combined with integrated dispersive D-wavelength analysis. int The principle involves calculating the dispersion curve of a helical microcavity to determine its waveguide parameters and achieve anomalous waveguide dispersion. The spacing between the first and second helical curved waveguides is determined through coupled simulation using the finite-difference time-domain method.

[0022] Step 2: Draw the first helical bend waveguide. Based on the designed waveguide parameters and waveguide spacing, use Archimedes' spiral formula (1-2) to calculate the a1 and b1 values ​​of the first helical bend waveguide, and give the initial angle θ. 01 and termination angle θ E1 The helical curved waveguide is plotted according to Archimedes' spiral formula (1-2). Here, a1 is the polar radius of the first helical curved waveguide when θ is 0, b1 is the change in polar radius of the first helical curved waveguide for every 1° rotation, and θ... 01 Let θ be the starting angle of the rotation. E1 The angle at which the rotation terminates is denoted.

[0023] Step 3: Draw the second helical bend waveguide. Based on the designed waveguide parameters and waveguide spacing, use Archimedes' spiral formula (1-2) to calculate the a2 and b2 values ​​of the second helical bend waveguide, and give the initial angle θ. 02 and termination angle θ E2 The helical curved waveguide is plotted according to Archimedes' spiral formula (1-2). Here, a2 is the polar radius of the second helical curved waveguide when θ is 0, b2 is the change in polar radius of the second helical curved waveguide for every 1° rotation, and θ... 02 Let θ be the starting angle of the rotation. E2 Let θ be the termination angle of the rotation. And satisfy b2 = b1, θ 02 With θ 01 The difference is an integer multiple of 180°.

[0024] Step 4: Draw the internal connecting waveguide. Based on the starting point coordinates of the first and second helical bend waveguides, calculate the radius of curvature at that point using the Archimedean spiral radius of curvature formula (1-4). The internal connecting waveguide consists of multiple Euler spiral waveguides, with the same coordinate position and radius of curvature at the connection points of each Euler spiral waveguide.

[0025] Archimedes' formula for the radius of curvature of a spiral (1-4)

[0026]

[0027] Where a represents the polar radius when θ is 0, b represents the change in polar radius for every 1° of rotation, and θ represents the total angle rotated.

[0028] Step 5: Draw the external connection waveguide. Based on the coordinates of the termination points of the first and second helical bend waveguides, calculate the radius of curvature at those points using the Archimedean spiral radius of curvature formula (1-4). Determine the Euler spiral parameters based on this radius of curvature. Determine the arc radius and central angle range based on the radius of curvature at the endpoint of the Euler spiral. Utilizing the characteristic that the Euler spiral has a point of zero curvature, connect the Euler bend waveguide to the straight waveguide.

[0029] Step 6: Calculate the lengths of the internal and external connecting waveguides.

[0030] Step 7: Calculate the effective length of the microcavity for the designed repetition frequency using the free spectral range formula (1-1). The effective length of the helical microcavity is: L = L (第一螺旋弯曲波导) +L (第二螺旋弯曲波导) +L (内部连接波导3) +L (外部连接波导4)

[0031] Step 8: Calculate the termination angles of the first and second helical bend waveguides, and redraw the helical bend waveguides. Since the starting angle remains unchanged, it does not affect the position of the internal connecting waveguides.

[0032] Step Nine: Based on the redrawn helical curved waveguides, calculate the curvature radii at the termination points of the first and second helical curved waveguides, and adjust the curvature radius and coordinates of the connection point between the external connecting curved waveguide and the first and second helical curved waveguides. Adjust the position of the external connecting waveguide; ensure that both ends of the external connecting curved waveguide are at the same coordinate positions as the termination points of the first and second helical curved waveguides, thus obtaining a low-repetition-frequency helical microcavity.

[0033] Beneficial effects:

[0034] 1. This invention discloses a low-repetition-rate (PRF) helical microcavity structure and its design method. The low-PRF helical microcavity structure comprises a first helical bent waveguide, a second helical bent waveguide, an internally connected bent waveguide, an externally connected bent waveguide, and a bus waveguide. The first helical bent waveguide, the second helical bent waveguide, and the internally connected bent waveguide satisfy a gradual change in radius of curvature at each point, which can prevent crosstalk of higher-order modes during optical transmission and reduce waveguide loss. The externally connected bent waveguide includes three types: straight waveguide, Euler bent waveguide, and circular arc waveguide, which can connect the termination points of the first and second helical bent waveguides to form a micro-ring cavity.

[0035] 2. The present invention discloses a low repetition rate spiral microcavity structure and design method. The internal connecting curved waveguide is designed according to the Euler spiral formula and is composed of multiple Euler spiral waveguide segments spliced ​​together. The splicing points of adjacent Euler spiral waveguides satisfy the same coordinates (x, y) and the same radius of curvature, thereby ensuring that the radius of curvature changes continuously and slowly at all points of the internal connecting curved waveguide, and there are no regions with abrupt changes in the radius of curvature. This effectively reduces optical mode mismatch loss and thus reduces the optical transmission loss of the spiral microcavity.

[0036] 3. The present invention discloses a low repetition rate spiral microcavity structure and design method. The first spiral bent waveguide and the second spiral bent waveguide are arranged using the Archimedes spiral formula to increase the effective length of the waveguide while reducing the area, thereby improving the chip area utilization rate of the low repetition rate spiral microcavity structure. Moreover, the design is an adiabatic bending curve that satisfies the gradual change of curvature radius, which can effectively prevent crosstalk of higher-order modes and effectively reduce the crosstalk loss of the microcavity waveguide.

[0037] 4. The present invention discloses a low repetition frequency helical microcavity structure and design method, which adopts a shared internal connecting curved waveguide for helical microcavities with different repetition frequencies. By simply changing the termination angle of the first and second helical curved waveguides and adjusting the curvature of the Euler curved waveguides at both ends of the external connecting waveguide, it is possible to efficiently design the structure of helical microcavities with different repetition frequencies.

[0038] 5. The present invention discloses a low repetition rate helical microcavity structure and design method, wherein the core material of the first helical bent waveguide, the second helical bent waveguide, the internal connecting bent waveguide, the external connecting bent waveguide, and the bus waveguide is selected as silicon nitride; according to the material properties of silicon nitride, it has a transparent window in the range of 400nm to 3.5μm, which enables its use in the visible light to mid-infrared range, and can be applied to fields such as chip optical clocks, on-chip narrow linewidth lasers, and on-chip optical frequency combs.

[0039] 6. The present invention discloses a low repetition rate spiral microcavity structure and design method, which designs the externally connected curved waveguide as a figure-9 structure, thereby reducing the area of ​​the low repetition rate spiral microcavity structure and improving the chip area utilization rate of the low repetition rate spiral microcavity. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a traditional ring-shaped microcavity, which consists of a circular waveguide ring and a straight waveguide.

[0041] Figure 2 This is a schematic diagram of a low-repetition-rate spiral microcavity structure according to the present invention.

[0042] Figure 3 This is a design flowchart of a low-repetition-rate spiral microcavity structure according to the present invention.

[0043] Figure 4 This is a schematic diagram of the cross-section of a helical bent waveguide, an example of the present invention.

[0044] Figure 5 This is the resonance peak of the silicon nitride spiral microcavity, an example of the present invention.

[0045] Wherein: 1—first helical bend waveguide, 2—second helical bend waveguide, 3—internal connecting bend waveguide, 4—external connecting bend waveguide, 5—bus waveguide. Detailed Implementation

[0046] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0047] Example 1:

[0048] like Figure 1 The diagram shows a traditional ring microcavity structure, consisting of a circular ring waveguide and a straight waveguide. The relationship between the repetition frequency and radius of this ring microcavity satisfies the free spectral range formula. When the repetition frequency of the ring microcavity is 10 GHz, the radius of the circular ring waveguide can be calculated to be approximately 2.3 mm using the free spectral range.

[0049] The formula for the free spectral range is shown in equation (1-1).

[0050]

[0051] Where Δλ represents the FSR of the optical microcavity, L eff n is the length of the optical microcavity. g (λ) is the group refractive index of the waveguide, λ is the wavelength of light, and n eff The effective refractive index.

[0052] like Figure 2As shown, this embodiment discloses a low repetition rate helical microcavity structure, including a first helical bent waveguide 1, a second helical bent waveguide 2, an internally connected bent waveguide 3, an externally connected bent waveguide 4, and a bus waveguide 5. The first helical bent waveguide 1 is a helical bent waveguide 1 with a gradually changing radius of curvature, and the second helical bent waveguide 2 is a helical bent waveguide 2 with a gradually changing radius of curvature. Figure 4 This is a schematic cross-sectional view of the first helical bent waveguide 1 and the second helical bent waveguide 2. The lower and upper cladding layers are made of silicon dioxide, and the waveguide core is made of silicon nitride. The waveguide width is 1.6 μm, the height is 800 nm, and the spacing between adjacent waveguides is 1.6 μm. This example uses a thick-film silicon nitride single-mode waveguide, but this design is also applicable to weakly bound silicon nitride waveguides and multimode silicon nitride waveguides. Furthermore, because this design is based on a helix with a gradually changing radius of curvature, it has a better effect on reducing loss and improving the quality factor for microcavities composed of weakly bound multimode silicon nitride waveguides. The internal connecting bent waveguide 3 has a waveguide width of 1.6 μm, a waveguide height of 800 nm, and a waveguide core made of silicon nitride. The radius of curvature at each point varies with the length and satisfies the Euler spiral equation. It is used as the starting point to connect the first helical bent waveguide 1 and the second helical bent waveguide 2. The external connecting bent waveguide 4 has a waveguide width of 1.6 μm and a waveguide height of 800 nm. Its core layer is made of silicon nitride and it serves as the endpoint connecting the first helical bent waveguide 1 and the second helical bent waveguide 2. The first helical bent waveguide 1, the second helical bent waveguide 2, the internal connecting bent waveguide 3, and the external connecting bent waveguide 4 form a closed helical ring waveguide. The bus waveguide 5 is used to transmit the pump laser emission beam, and the beam transmitted in the bus waveguide 5 is coupled into the helical ring waveguide.

[0053] Furthermore, the beam emitted by the pump laser is transmitted through bus waveguide 5, and a portion of the light transmitted through bus waveguide 5 is coupled into the helical ring waveguide. The effective length of the closed helical ring waveguide, formed by the first helical bent waveguide 1, the second helical bent waveguide 2, the internally connected bent waveguide 3, and the externally connected bent waveguide 4, is calculated according to the free spectral range formula. When the repetition frequency is 10 GHz, the effective length of the closed helical ring waveguide is 1430.06 μm. The first helical bent waveguide 1 and the second helical bent waveguide 2 are structurally arranged using Archimedes' spiral formula. The initial angle θ of the first helical bent waveguide 1... 01 The value is 9000 rad, and the termination angle is θ. E1 The initial curvature radius is 11111 rad, the initial radius of curvature is approximately 157 μm, and the final radius of curvature is approximately 193.9 μm. The initial angle θ of the second helical curved waveguide 2 is... 01 It is 8820 rad, and the termination angle is θ. E1The effective waveguide length is 10800 rad, with a starting point radius of curvature of approximately 163 μm and a ending point radius of curvature of approximately 197.8 μm. This achieves a reduction in area while increasing the effective waveguide length, thereby improving the chip area utilization of the low-repetition-rate spiral microcavity structure. Part of the light coupled into the spiral ring waveguide from the bus waveguide 5 propagates between the first spiral bent waveguide 1, the second spiral bent waveguide 2, the internally connected bent waveguide 3, and the externally connected bent waveguide 4, resulting in resonance and a resonance peak in the output spectrum. Figure 5 The resonant peak of the silicon nitride helical microcavity is an example of the present invention. Specifically: during the propagation of the resonant light in the first helical bent waveguide 1, the gradual change in the waveguide curvature radius effectively reduces crosstalk loss of higher-order modes during resonant light propagation; during propagation in the second helical bent waveguide 2, the gradual change in the waveguide curvature radius further reduces crosstalk loss of higher-order modes during resonant light propagation; and during propagation in the internally connected bent waveguide 3, the absence of a step change in curvature radius within the waveguide reduces optical mode mismatch loss, thereby reducing the optical transmission loss of the helical microcavity.

[0054] The formula for the free spectral range is shown in equation (1-1).

[0055]

[0056] Where Δλ represents the FSR of the optical microcavity, L eff n is the length of the optical microcavity. g (λ) is the group refractive index of the waveguide, λ is the wavelength of light, and n eff The effective refractive index.

[0057] The formula for the Archimedes spiral is shown in equation (1-2).

[0058] x=(a+bθ)cosθ (1-2)

[0059] y = (a + bθ)·sinθ

[0060] Where a represents the polar radius when θ is 0, b represents the change in polar radius for every 1° of rotation, θ represents the total angle rotated, and the spacing between the spirals is 2πb.

[0061] Furthermore, the internally connected curved waveguide 3 is designed according to the Euler spiral formula (1-3), with a total length of approximately 543.3 μm. It is composed of multiple Euler spiral waveguide segments spliced ​​together. The splicing points of adjacent Euler spiral waveguides satisfy the same coordinates (x, y) and the same radius of curvature, thereby ensuring that the radius of curvature of the internally connected curved waveguide 3 changes continuously and slowly at all points, without any abrupt changes in the radius of curvature. Moreover, the change in the radius of curvature at each point exhibits multiple change modes, such as gradually increasing, gradually decreasing, and then gradually increasing again.

[0062] The formula for the Euler spiral is shown in equation (1-3).

[0063]

[0064] Furthermore, the externally connected bent waveguide 4 is composed of three types of waveguides: straight, Euler bend, and circular arc, with a total length of approximately 753.1 μm. There are a few abrupt changes in the radius of curvature at the connection points between the Euler bend and the circular arc waveguides, while there are no such abrupt changes at the connection points between the straight and Euler bend waveguides. The radius of curvature at these abrupt changes varies within a range of approximately (5–8) μm. To reduce the area of ​​the low-repetition-rate helical microcavity structure and improve the chip area utilization of the low-repetition-rate helical microcavity, the externally connected bent waveguide 4 is designed as a figure-9 structure.

[0065] Furthermore, the core material of the first helical bent waveguide 1, the second helical bent waveguide 2, the internal connecting bent waveguide 3, the external connecting bent waveguide 4, and the bus waveguide 5 is preferably silicon nitride. Based on the material properties of silicon nitride: it has a transparent window in the range of 400nm to 3.5μm, enabling its use in the visible light to mid-infrared range, meeting the needs of most applications; it has a high nonlinear coefficient and a lower threshold for exciting nonlinear effects, making silicon nitride suitable for the fabrication of microcavity chips.

[0066] like Figure 3 As shown in the figure, this embodiment discloses a design method for a low repetition rate helical microcavity structure, used to design the aforementioned low repetition rate helical microcavity structure. The specific implementation steps of the design method for a low repetition rate helical microcavity structure are as follows:

[0067] Step 1: Determine the waveguide parameters and waveguide spacing of the helical microcavity. The waveguide widths of the first helical bent waveguide 1, the second helical bent waveguide 2, the internally connected bent waveguide 3, and the externally connected bent waveguide 4 are analyzed based on the waveguide characteristics using the finite element method, combined with integrated dispersion D. int The principle involves calculating the dispersion curve of the helical microcavity to determine the waveguide parameters as a width of 1.6 μm and a height of 800 nm, thus achieving anomalous waveguide dispersion. Coupled simulation calculations of the spacing between the first helical curved waveguide 1 and the second helical curved waveguide 2 are performed using the finite-difference time-domain method, determining the waveguide spacing to be 1.6 μm.

[0068] Step 2: Draw the first helical curved waveguide 1. Based on the designed waveguide parameters and waveguide spacing, use Archimedes' spiral formula (1-2) to calculate the a1 and b1 values ​​of the first helical curved waveguide 1, and give the initial angle θ. 01 9000 rad and termination angle θ E1 Given a radius of 12600 rad, a helical curved waveguide is plotted according to Archimedes' spiral formula (1-2). Here, a1 is the polar radius of the first helical curved waveguide 1 when θ is 0, b1 is the change in polar radius of the first helical curved waveguide 1 for every 1° rotation, and θ...01 Let θ be the starting angle of the rotation. E1 The angle at which the rotation terminates is denoted.

[0069] Step 3: Draw the second helical curved waveguide 2. Based on the designed waveguide parameters and waveguide spacing, use Archimedes' spiral formula (1-2) to calculate the values ​​of a2 and b2 of the second helical curved waveguide 2, and give the initial angle θ. 02 8820 rad and termination angle θ E2 Given a radius of 12554 rad, the helical curved waveguide is plotted according to Archimedes' spiral formula (1-2). Here, a2 is the polar radius of the second helical curved waveguide 2 when θ is 0, b2 is the change in polar radius of the second helical curved waveguide 2 for every 1° rotation, and θ... 02 Let θ be the starting angle of the rotation. E2 Let θ be the termination angle of the rotation. And satisfy b2 = b1, θ 02 With θ 01 The difference is an integer multiple of 180°.

[0070] Step 4: Draw the internal connecting waveguides. Based on the starting point coordinates of the first helical bend waveguide 1 and the second helical bend waveguide 2, and using the Archimedean spiral radius of curvature formula (1-4), calculate the radii of curvature at these points to be 157 μm and 163 μm, respectively. The internal connecting waveguides consist of multiple Euler spiral waveguides, with the same coordinate position and radius of curvature at the connection points of each Euler spiral waveguide.

[0071] Archimedes' formula for the radius of curvature of a spiral (1-4)

[0072]

[0073] Where a represents the polar radius when θ is 0, b represents the change in polar radius for every 1° of rotation, and θ represents the total angle rotated.

[0074] Step 5: Draw the external connection waveguides. Based on the coordinates of the termination points of the first helical curved waveguide 1 and the second helical curved waveguide 2, calculate the radius of curvature at those points using the Archimedean spiral radius of curvature formula (1-4), and determine the Euler spiral parameters based on this radius of curvature. Based on the radius of curvature at the endpoint of the Euler spiral, determine the arc radius as 75.6 μm and the range of the central angle. Utilizing the characteristic that the Euler spiral has a point of zero curvature, connect the Euler curved waveguide to the straight waveguide.

[0075] Step 6: Calculate the lengths of the internal and external connecting waveguides, which are 543.3 μm and 753.1 μm, respectively.

[0076] Step 7: Calculate the effective length of the microcavity for the designed repetition frequency using the free spectral range formula (1-1). The effective length of the helical microcavity is: L = L(第一螺旋弯曲波导1) +L (第二螺旋弯曲波导2) +L (内部连接波导3) +L (外部连接波导4) When the repetition frequency is 10 GHz, the effective length of the helical microcavity is calculated to be 1430.06 μm according to the free spectral range formula, and the required helical waveguide length is approximately 1300.4 μm.

[0077] Step 8: Calculate the termination angles of the first helical bend waveguide 1 and the second helical bend waveguide 2, which are 11111 rad and 10800 rad respectively, and redraw the helical bend waveguides. Since the starting angle has not changed, it does not affect the position of the internal connecting waveguides.

[0078] Step 9: Based on the curvature radii at the endpoints of the redrawn helical curved waveguides (193.9 μm and 197.8 μm respectively), adjust the curvature radii and coordinates of the Euler curved waveguides at both ends of the external connecting curved waveguide. This ensures that the endpoint coordinates of the external connecting curved waveguide are the same as those of the first and second helical curved waveguides, completing the rendering of the helical microcavity with a repetition frequency of 10 GHz. The area of ​​this helical microcavity structure is approximately 0.544 mm × 0.402 mm.

[0079] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method of a low repetition rate spiral microcavity structure, for designing a low repetition rate spiral microcavity structure, characterized in that: The low repetition frequency spiral microcavity structure comprises a first spiral curved waveguide (1), a second spiral curved waveguide (2), an internal connecting curved waveguide (3), an external connecting curved waveguide (4) and a bus waveguide (5); the first spiral curved waveguide (1) is a first spiral curved waveguide (1) with a gradually changed curvature radius, and the second spiral curved waveguide (2) is a second spiral curved waveguide (2) with a gradually changed curvature radius; the curvature radius of each point of the internal connecting curved waveguide (3) changes with the length and satisfies the Euler spiral equation, and the internal connecting curved waveguide (3) is used for connecting the starting point of the first spiral curved waveguide (1) and the second spiral curved waveguide (2); the external connecting curved waveguide (4) is used for connecting the terminal point of the first spiral curved waveguide (1) and the second spiral curved waveguide (2); the first spiral curved waveguide (1), the second spiral curved waveguide (2), the internal connecting curved waveguide (3) and the external connecting curved waveguide (4) form a closed spiral ring type waveguide; the bus waveguide (5) is used for transmitting a pump laser emission beam, and the light beam transmitted in the bus waveguide (5) is coupled into the spiral ring type waveguide; The design method comprises the following steps, Step one: determine the waveguide parameters and waveguide spacing of the spiral microcavity; the waveguide width of the first spiral curved waveguide (1), the second spiral curved waveguide (2), the internal connecting curved waveguide (3) and the external connecting curved waveguide (4) is analyzed according to the finite element method, the integrated dispersion D int Principle, calculate the dispersion curve of the spiral microcavity, determine the waveguide parameters of the spiral microcavity, realize the abnormal dispersion of the waveguide; the spacing of the first spiral curved waveguide (1) and the second spiral curved waveguide (2) is coupled and simulated by using the finite difference time domain method, and the waveguide spacing is determined; Step two: draw the first spiral curved waveguide (1); according to the designed waveguide parameters and waveguide spacing, the a1 value and b1 value of the first spiral curved waveguide (1) are calculated by using the Archimedes spiral formula, and the starting angle θ 01 and the ending angle θ E1 are given, and the spiral curved waveguide drawing is realized according to the Archimedes spiral formula; wherein a1 is the polar radius of the first spiral curved waveguide (1) when θ is 0, b1 is the change amount of the polar radius of the first spiral curved waveguide (1) when it rotates 1°, θ 01 is the starting angle of rotation, and θ E1 is the ending angle of rotation; Step three: draw the second spiral curved waveguide (2); according to the designed waveguide parameters and waveguide spacing, the a2 value and b2 value of the second spiral curved waveguide (2) are calculated by using the Archimedes spiral formula, and the starting angle θ 02 and the ending angle θ E2 are given, and the spiral curved waveguide is drawn according to the Archimedes spiral formula; wherein a2 is the polar radius of the second spiral curved waveguide (2) when θ is 0, b2 is the change amount of the polar radius of the second spiral curved waveguide (2) when it rotates 1°, θ 02 is the starting angle of rotation, θ E2 is the ending angle of rotation; and b2 = b1, the difference between θ 02 and θ 01 is an integral multiple of 180°. Step four: drawing the internal connecting curved waveguide (3); the curvature radius at the starting point of the first spiral curved waveguide (1) and the second spiral curved waveguide (2) is calculated according to the starting point coordinates and the Archimedes spiral curvature radius formula (1-4); the internal connecting waveguide is composed of a plurality of Euler spiral waveguides, the connecting point coordinates of each Euler spiral waveguide are the same, and the curvature radius is the same; Archimedes spiral curvature radius formula (1-4) Wherein, a represents the polar radius when θ is 0, b represents the change amount of the polar radius when rotating 1°, and θ represents the total angle of rotation. Step five: drawing the external connecting curved waveguide (4); the curvature radius at the terminal point of the first spiral curved waveguide (1) and the second spiral curved waveguide (2) is calculated according to the terminal point coordinates and the Archimedes spiral curvature radius formula (1-4), and the Euler spiral parameter is determined according to the curvature radius; the circular arc radius and the central angle range are determined according to the curvature radius of the terminal point position of the Euler spiral, and the connection between the Euler spiral waveguide and the straight waveguide is realized by using the characteristic that the Euler spiral has a point with a curvature of 0; Step six: calculating the length of the internal connecting waveguide and the external connecting waveguide; Step seven: calculate the effective length of the designed repetition frequency microcavity according to the free spectral range formula; the effective length of the spiral microcavity is: L = L (第一螺旋弯曲波导(1)) +L (第二螺旋弯曲波导(2)) +L (内部连接波导3) +L (外部连接波导4) Step eight: calculating the terminal angle of the first spiral curved waveguide (1) and the second spiral curved waveguide (2), and redrawing the spiral curved waveguide; since the starting angle does not change, the position of the internal connecting waveguide is not affected; Step nine: according to the redrawing spiral curved waveguide, the terminal point curvature radius of the first spiral curved waveguide (1) and the second spiral curved waveguide (2) is calculated, and the curvature radius and coordinates of the connecting point of the external connecting curved waveguide (4) connecting the first spiral curved waveguide (1) and the second spiral curved waveguide (2) are adjusted; the terminal point coordinates of the external connecting curved waveguide (4) at both ends are the same as those of the first spiral curved waveguide (1) and the second spiral curved waveguide (2), that is, a low repetition frequency spiral microcavity is obtained.

2. The method for designing a low repetition rate spiral microcavity structure according to claim 1, wherein: The light beam emitted by the pump laser is transmitted through the bus waveguide (5), and part of the light transmitted by the bus waveguide (5) is coupled into the spiral ring waveguide; the closed spiral ring waveguide formed by the first spiral curved waveguide (1), the second spiral curved waveguide (2), the internal connecting curved waveguide (3) and the external connecting curved waveguide (4) has an effective length calculated according to the free spectral range formula, and the first spiral curved waveguide (1) and the second spiral curved waveguide (2) are arranged according to the Archimedes spiral formula, so that the effective length of the waveguide is increased while the area is reduced, and the chip area utilization rate of the low repetition frequency spiral microcavity structure is improved; the part of the light coupled into the spiral ring waveguide by the bus waveguide (5) is transmitted between the first spiral curved waveguide (1), the second spiral curved waveguide (2), the internal connecting curved waveguide (3) and the external connecting curved waveguide (4), resonates and generates a resonance peak in the output spectrum; wherein: during the transmission of the resonant light in the first spiral curved waveguide (1), the radius of curvature of the waveguide gradually changes, thereby effectively reducing the crosstalk loss of high-order modes in the transmission process of the resonant light; during the transmission of the resonant light in the second spiral curved waveguide (2), the radius of curvature of the waveguide gradually changes, thereby reducing the crosstalk loss of high-order modes in the transmission process of the resonant light; during the transmission of the resonant light in the internal connecting curved waveguide (3), there is no step change in the radius of curvature inside the waveguide, thereby reducing the optical mode mismatch loss and further reducing the optical transmission loss of the spiral microcavity. The free spectral range formula is as formula (1-1) where Δλ represents the FSR of the optical microcavity, L eff is the length of the optical microcavity, n g (λ) is the group refractive index of the waveguide, and λ is the optical wavelength. The Archimedes spiral formula is as formula (1-2) x = (a + b·θ)·cosθ (1-2) y = (a + b·θ)·sinθ Wherein, a represents the polar radius when θ is 0, b represents the change amount of the polar radius per 1° rotation, θ represents the total angle of rotation, and the pitch of the spiral is 2πb.

3. The method of designing a low repetition rate spiral microcavity structure according to claim 2, wherein: The internal connecting curved waveguide (3) is designed according to the Euler spiral formula (1-3) and is spliced by multiple Euler spiral waveguides, the splicing points of adjacent Euler spiral waveguides satisfy the same coordinates (x, y) and the same radius of curvature, thereby ensuring that the internal connecting curved waveguide (3) satisfies the continuous and slow change of the radius of curvature everywhere, there is no area with sudden change of the radius of curvature, and the radius of curvature at each point gradually changes from large to small and then to large. The Euler spiral formula is as formula (1-3) 4. The method of designing a low repetition rate spiral microcavity structure according to claim 2, wherein: The external connecting curved waveguide (4) is designed as a "9" type structure, which is composed of straight lines, Euler spirals and circular arcs, and the radius of curvature of the waveguide connection between the Euler spiral and the circular arc changes suddenly, and the radius of curvature of the waveguide connection between the straight line and the Euler spiral does not change suddenly; the change range of the radius of curvature at the sudden change position is 5-8μm.

5. The method of designing a low-repetition-rate spiral microcavity structure according to claim 2, wherein: The core layer material of the first spiral curved waveguide (1), the second spiral curved waveguide (2), the internal connecting curved waveguide (3), the external connecting curved waveguide (4) and the bus waveguide (5) is selected as silicon nitride; according to the material properties of silicon nitride: it has a transparent window in the range of 400nm-3.5μm, which can be used in the visible light to mid-infrared range.

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